We discuss connections between the strong ellipticity condition and the infinitesimal instability within the nonlinear strain gradient elasticity. The strong ellipticity (SE) condition describes the property of equations of statics whereas the infinitesimal stability is introduced as the positive definiteness of the second variation of an energy functional. Here we establish few implications which simplify the further analysis of stability using formulated SE conditions. The results could be useful for the analysis of solutions of homogenized models of beam-lattice materials at different scales.
Strong ellipticity conditions and infinitesimal stability within nonlinear strain gradient elasticity
Eremeyev V. A.
2021-01-01
Abstract
We discuss connections between the strong ellipticity condition and the infinitesimal instability within the nonlinear strain gradient elasticity. The strong ellipticity (SE) condition describes the property of equations of statics whereas the infinitesimal stability is introduced as the positive definiteness of the second variation of an energy functional. Here we establish few implications which simplify the further analysis of stability using formulated SE conditions. The results could be useful for the analysis of solutions of homogenized models of beam-lattice materials at different scales.File in questo prodotto:
File | Dimensione | Formato | |
---|---|---|---|
Eremeyev_MRC2021_Ellipticity.pdf
Solo gestori archivio
Tipologia:
versione editoriale (VoR)
Dimensione
557.86 kB
Formato
Adobe PDF
|
557.86 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.